Permeability of a porous material with a fluid interface is shown to be related to the propagation of the slow longitudinal wave. The propagation threshold of the slow longitudinal wave occurs when the wave number is higher than the critical wave number, k(cr). Measuring k(cr) can provide the intrinsic permeability of a porous interface. The ability to detect a change in k(cr) due to differences in pore size and fluid viscosity is demonstrated. This measurement is demonstrated in a model material with two pore sizes and two fluid viscosities. The results suggest opportunities to extend the method to a range of materials of scientific and technical importance.